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SAT Math skill page

SAT Area and Volume Practice

Choose the right formula, track units, and separate area from volume.

Practice area and volume in Dolphin SATPractice questions
10-16 min practice time3 questions on pageGeometry
Practice time10-16 min
Practice questions3 questions
Best forGeometry

What this tests

What to know for this SAT skill

When can you square or cube a scale factor?

Use the square or cube rule only when the figures are similar: every corresponding length must change by the same positive factor. A change to just one dimension does not establish similarity.

What if only one dimension changes?

Start from the formula and keep unchanged dimensions fixed. In a rectangular prism, volume is length times width times height. Multiplying only its height by a factor multiplies its volume by that factor, not its cube. Surface area needs its own calculation because not every face changes in the same way.

How do you check the comparison?

Compare corresponding lengths in the same units and in the same direction, new divided by original. Check every required dimension before applying a common factor. Distinguish a length ratio from an area or volume ratio; they are not interchangeable.

Topic reference: College Board SAT Math specifications: geometry, similarity and scale factors. Guidance reviewed .

Dolphin practice questions

Practice your skill

Question 1 of 3Easy
A rectangle has length 8 and width 5. What is its area?
  1. 13
  2. 26
  3. 40
  4. 80
Show answer and solution
Correct answerC. 40

Solution walkthrough

  1. Area of a rectangle is length times width: 8 * 5 = 40.
Question 2 of 3Medium
A triangle has base 12 and height 7. What is its area?
  1. 19
  2. 42
  3. 84
  4. 98
Show answer and solution
Correct answerB. 42

Solution walkthrough

  1. Triangle area is one-half base times height: (1/2)(12)(7) = 42.
Question 3 of 3Hard
A rectangular prism has dimensions 3, 4, and 10. What is its volume?
  1. 17
  2. 34
  3. 120
  4. 240
Show answer and solution
Correct answerC. 120

Solution walkthrough

  1. Volume is length times width times height: 3 * 4 * 10 = 120 cubic units.

Avoid these traps

Common mistakes on this skill

Using a perimeter formula for area

Perimeter measures boundary length, area measures a two-dimensional region, and volume measures three-dimensional space.

Forgetting squared or cubed units

Area uses square units and volume uses cubic units; the units are part of the result.

Study plan

How to practice this skill in Dolphin

  1. Sketch and label the dimensions, including any hidden radius, height, or shared side.
  2. Choose the formula that matches the requested measure rather than the pictured shape alone.
  3. Substitute consistently converted dimensions and check the final units.
Practice area and volume in Dolphin SAT

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FAQ

Questions about SAT Area and Volume Practice

How do scale factors affect area and volume?

For similar figures, when every corresponding length is multiplied by the same positive scale factor k, area is multiplied by k squared and volume by k cubed. If only one dimension changes, use the relevant formula instead of automatically squaring or cubing the factor.

Is the SAT formula sheet enough for these questions?

It supplies many formulas, but you still need to identify the correct dimensions and whether the question asks for area, surface area, or volume.